How to speed up only a part of an animation?
I make an edit as it looks like you don't need to use a Follow Path constraint and a simple parentage is enough. 


So, once you parented the object (in your case, the penguin's armature) to your curve, you will just play with the Evaluation Time value of your object, in the Properties panel > Data > Path Animation..
Go in the Properties panel > Data > Path Animation.
Select the Frames rate you want, 100 is good.
In the Timeline (or Dopesheet) window, point the cursor where you want the animation to begin, for example frame 1.
For this frame 1, choose the object position along the curve with the Evaluation Time value. Once it's good for you, put your mouse over the Evaluation Time value and press i to insert a keyframe.
Again, in the Timeline (or Dopesheet) window, point the cursor where you want the animation to change speed, for example frame 50.
For this frame 50, choose the object position along the curve with the Evaluation Time value. Once it's good for you, insert a keyframe with i.
Etc, etc, you can make your penguin move forward, backward, etc, at the speed you want.
You can change the transitions in the Graph Editor with T > Interpolations.




old answer, with the Follow Path constraint:

The speed has been automatically generated when you gave your object a Follow Path constraint. If you want to vary the speed of the object along the path, you need to:


Select the path, open the Graph Editor, on the left panel, unfold the BezierCurve menu and click on Evaluation Time.
On the right panel of the Graph Editor, Modifiers tab, you'll now see the Generator box that has been generated by the constraint. Delete it. Now your object don't move any more, but you'll be able to determine its speed manually.
Keep the path selected and go in the Properties panel > Data > Path Animation. If you change the Evaluation Time value you can see that the object moves along the curve.
Select the Frames rate you want, 100 is good.
In the Timeline (or Dopesheet) window, point the cursor where you want the animation to begin, for example frame 1.
For this frame 1, choose the object position along the curve with the Evaluation Time value. Once it's good for you, insert a keyframe with i.
Again, in the Timeline (or Dopesheet) window, point the cursor where you want the animation to change speed, for example frame 50.
For this frame 50, choose the object position along the curve with the Evaluation Time value. Once it's good for you, insert a keyframe with i.
Etc.